Answers
Check the picture below.
so from the picture we can pretty much tell two solutions or zeros and another point where it passes up above, so
[tex]\begin{cases} x=-1\implies &x+1=0\\\\ x=7\implies &x-7=0 \end{cases}\hspace{8em} \begin{array}{llll} a(x+1)(x-7)=0\\\\ a(x+1)(x-7)=y \end{array} \\\\[-0.35em] ~\dotfill\\\\ \textit{we also know that} \begin{cases} x=5\\ y=3 \end{cases}\implies a(5+1)(5-7)=3 \\\\\\ a(6)(-2)=3\implies -12a=3\implies a=\cfrac{3}{-12}\implies a=-\cfrac{1}{4} \\\\[-0.35em] ~\dotfill[/tex]
[tex]-\cfrac{1}{4}(x+1)(x-7)=y\implies -\cfrac{1}{4}\stackrel{F~O~I~L}{(x^2-6x-7)}=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} -\cfrac{x^2}{4}+\cfrac{3x}{2}+\cfrac{7}{4}=y \end{array}}~\hfill[/tex]
Related Questions
The equation of Line 1 is y=-2x + 7. Line 2 passesthrough the points (2, 3) and (4, 4). Which statementis true about Line 1 and Line 2?Line 1 and Line 2 are perpendicularO Line 1 is longer than Line 2Line 1 has the same y-intercept as Line 2Line 1 and Line 2 are parallel
Answers
SOLUTION
Line 1 is given as
[tex]y=-2x+7[/tex]let's find the equation of line 2, it passes through points (2, 3) and (4, 4)
The slope is
[tex]\begin{gathered} m=\frac{4-3}{4-2} \\ m=\frac{1}{2} \end{gathered}[/tex]The slope of line 2 is 1/2
If the two lines are perpendicular, then the product of their slope will be = -1, that is
[tex]\begin{gathered} m_1m_2=-1 \\ slope\text{ of line 1 m}_1=-2 \\ slope\text{ of line 2, m}_2=\frac{1}{2} \\ -2\times\frac{1}{2}=\frac{-2}{2}=-1 \\ \end{gathered}[/tex]Since the product of their slope = -1
Hence Line 1 and Line 2 are perpendicular
Geometry homework
Please help me figure this out
Answers
According to the solving the space between Arthur and Jamie are 39.1 meters.
What is a coordinate system?A coordinate system is a method for determining how to place points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.
how to locate Distance between two points?The length of the line segment bridging two locations in a plane is known as the distance between them. d=√((x2 – x1)² + (y2 – y1)²). is a typical formula for determining the separation between two places. Any two sites on an x-y plane or coordinate plane can have their distance between them calculated using this equation.
According to the given data:location of Arthur is (20, 30)
location of Jamie is (45, 60)
Let's apply the rule of distance to determine how far away they are because we know that :
d = √((X₂ - X₁)² + (Y₂ - Y₁)²)
let substituting the value we get:
d = √((X₂ - X₁)² + (Y₂ - Y₁)²)
d = √((45 - 20)² + (60 - 30)²)
= √(25)² + (30)²)
= 39.1
According to the solving the space between Arthur and Jamie are 39.1 meters.
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can anyone help me with this
Answers
Step-by-step explanation:
Since area = 27cm²
area = 3 × (x + 4)
27 = 3(x + 4)
expand the right side
27 = 3x + 12
move 12 to the left side and subtract it with 27
15=3x
then divide both sides with 3
x=5
screenshot of question below
Answers
1. The slope is -2.
2. The slope is 1.
3. cost of 1 yards fabric is $6.49.
4. The average speed is 65 miles/ h.
What is slope?
The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as,
The slope of line is the measure of steepness or the direction of line the coordinate plane.
m = Δy/Δx
where, m is the slope
1. The co- ordinates of the graph is (0, 0) and (-1, 2)
slope = (2-0) / (-1 - 0) = 2/ (-1) = -2
Thus, the slope is -2.
2. The co-ordinates of the graph is (0, 0) and (4, 4)
slope = (4 - 0) / (4- 0) = 4/4 = 1
Thus, the slope is 1.
3. cost of 7 yards fabric = $45. 43
cost of 1 yards fabric = 45. 43/7
= $6.49
4. Distance = 325 miles
Time = 5 hours
So, average speed = 325 / 5
= 65 miles/ h
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Why do you think 900km is less than the perimeter of the of Bhutan (about 1075km)?
Answers
900km is less than the perimeter of the of Bhutan about 1075km.
Describe perimeter.The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.
The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. The surface of a shape's area is measured.
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A segment that is both an altitude and a median of a triangle is a?
Answers
A segment that is both an altitude and a median of a triangle is a perpendicular bisector.
A median is a segment from a vertex to the midpoint of the opposite side. There are of course three medians of a triangle; they’re concurrent, meeting at a point called the centroid.
An altitude is a segment through a vertex that’s perpendicular to the opposite side; the foot of the altitude (at the point of perpendicularity) either on the side or on the line resulting from extending the side. The three altitudes of a triangle are also concurrent, meeting at a point called the orthocenter.
And when both the altitude and a median of a triangle are the same, then it is called a perpendicular bisector.
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PLS answer asap, 100 points see attachment
Answers
The measures of the angles are given as follows:
1. p = 67º.
2. q = 27º.
Item 1To solve item 1, first we have to consider that the sum of the internal angles of a triangle is of 180º, hence we find angle x, which is the interval angle of angle p.
Hence:
x + 35 + 32 = 180
x + 67 = 180
x = 113º.
An angle and it's respective external angle are supplementary, meaning that the sum of it's measures are of 180º, hence:
p + x = 180
p + 113 = 180
p = 67º.
Item 2The internal angles are given as follows:
q.128º.180 - 155 = 25º.The sum of their measures is of 180º, hence we can simply solve for q as follows:
q + 128 + 25 = 180
q + 153 = 180
q = 27º.
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Answer:
The measures of the angles are given as follows:
1. p = 67º.
2. q = 27º.
Step-by-step explanation:
But you didn't have to cut me off
Make out like it never happened and that we were nothing (aah-ooh)
And I don't even need your love (ooh)
But you treat me like a stranger, and that feels so rough (aah)
No, you didn't have to stoop so low (ooh)
Have your friends collect your records and then change your number (aah)
I guess that I don't need that, though
Now you're just somebody that I used to know
(Theoretical Probability LC)
When given a set of cards laying face down that spell M, A, T, H, I, S, F, U, N, determine the probability of randomly drawing a consonant.
Answers
The probability of drawing a consonant from the given set of cards is 0.66.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
The given letters are M, A, T, H, I, S, F, U and N.
Total number of letters are 9.
The number of vowels is 3.
Then, the number of consonants is 9 - 3 =6.
Now, the probability for choosing consonant is given as follows,
P(Consonant) = Number of Consonants ÷ Total letters
⇒ 6/9 = 0.66
Hence, the probability of randomly drawing a consonant is given as 0.66.
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Answer: 6/10 is answer
Step-by-step explanation:
Just trust please
There are 25 birds and 12 ducks. Compare the number of birds to the total number of animals. Write you answer three ways. Your answer
Answers
Find out the total number of animals
25+12=37 animals
Compare the number of birds to the total number of animals
number of birds=25
so
25/37
or
25:37
or
25 to 37
Ashley is a software saleswoman. Her monthly salary is $2200 plus an additional $40 for every copy of math is fun she sells. Let S represent her total salary (In dollars), and let N represent the number of copies of math is fun she sells. Write an equation relating S to N and then graph your equation using the axes below
Answers
The equation of S in terms of N is S(N) = 2200 + 40N
How to determine the equation that relates S to NFrom the question, the given parameters are
Monthly salary = $2200
Additional earnings = $40 per copy of Math fun sold
The equation that relates S to N is then calculated as
Total = Monthly salary + Additional earnings x Number of copy of Math fun sold
Substitute the known values in the above equation
So, we have
S(N) = 2200 + 40N
So, the equation is S(N) = 2200 + 40N
See attachment for the graph
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is m parallel to n if so state the theorem you can use
Answers
If two lines and a transversal form corresponding angles that are congruent (shown by the marks in the angles) then the lines are parallel. Thus m and n are parallel.
Rewrite in simplest terms: -2(k+1)-6k
Answers
Answer:
-8k -2
Step-by-step explanation:
You want the simplified form of -2(k+1)-6k.
SimplificationThe process of simplifying an algebraic expression includes ...
removing parenthesescombining like termsParentheses are removed using the distributive property. The factor outside parentheses multiplies each term inside.
-2(k +1) -6k
= (-2)(k) +(-2)(1) -6k = -2k -2 -6k
Terms with the same variable content can be combined by adding their coefficients. (The distributive property is involved here, too.)
= (-2 -6)k -2 = -8k -2
The simplified expression is -8k -2.
PLEASE HELPPP (just need to know whether it’s discrete of continuous)
7. To meet the demands placed on them, the brick layers have started laying 5% more bricks
each day.
b. Linear or exponential, discrete or continuous?
exponential,
Answers
If the bricklayers lay 5% more blocks each day. The function is exponential and discrete.
What is a discrete and exponential function?
An exponential function is a function that increases or decreases at an increasing rate. It does not increase by a constant number.
The form of an exponential function: [tex]e^{x}[/tex]
Where:
• x = the variable
• e = constant
For example, the blocks layed on the first day is 100.
The bricks layed on the second day = 100 x (1.05) = 105 Bricks layed on the 10th day = 100 x (1.05)^9 = 55.13A discrete variable is a variable that assumes only a finite number of values. A discrete variable can be counted.
A linear function is a function that increases at a constant rate. For example, if the bricklayers lay 100 bricks every day, it can be modelled as a linear function.
A continous variable does not take on a finite number of values. It cannot be counted and it is instead measured.
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An inequality is shown below.
4x + 2<2x +9
Which graph shows the solution to the inequality?
O A
O
O
B. -
C.
OD
01
N
01
w.
0123
56
8 9 10
8 9 10
+
7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
Answers
Answer: Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x < 7/2
Step-by-step explanation: graph included in link
The graph which shows the solution of the inequality 4x + 2 < 2x + 9 is the graph B.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
The given linear in equality is,
4x + 2 < 2x + 9
Find the solution set of the inequality.
Operate the like terms together.
Subtracting both sides by 2x,
2x + 2 < 9
Subtracting both sides by 2,
2x < 7
Dividing both sides by 2,
x < 3.5
Hence the correct graph is B.
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Create an equation with one solution of x = −7
All help is appreciated :)
Answers
The most appropriate choice for linear equation will be given by -
8x - (x - 35) = 2x - (7 + x) is the required equation with x = -7
What is linear equation?
At first it is important to know about algebraic expression
Algebraic expression consist of numbers and variables connected with addition, subtraction, multiplication and division.
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Let y be filled in the gap
8x - (x -35) = 2x - (y + x)
8x - x + 35 = 2x - y - x
7x + 35 = x - y
putting x = -7
7(-7) + 35 = -7 -y
y = -49+35 + 7
y = 7
8x - (x - 35) = 2x - (7 + x) is the required equation with x = -7
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Write an equation of the line passing through point P(0, 0) that is perpendicular to the line y = -9x-1.
y =
Answers
The equation of the line passing through P(0, 0) perpendicular to y = -9x - 1 will be [tex]y = \frac{1}{9}x[/tex]
The given question states that the line passes through the point P(0, 0) perpendicular to the line y = -9x - 1. We have to find out the equation of the line. We have to find the equation in slope-intercept form.
We know the slope intercept is: y = mx + b
Also, given the perpendicular line has slope m₂ = -9 according to slope-intercept form. And we know that perpendicular lines have a slope that is equal to the negative reciprocal.
So, the Slope of the line m₁ = Negative reciprocal of the slope of the perpendicular line.
=> [tex]m_{1} = -\frac{1}{m_{2} }[/tex]
=> [tex]m_{1} = -\frac{1}{(-9)}[/tex]
=> [tex]m_{1} = \frac{1}{9 }[/tex]
We get the slope [tex]m_{1} = \frac{1}{9 }[/tex]. Also, it is given that the line passes through (0, 0) so the y-intercept b = 0. Putting these values in slope-intercept form, we get:
=> y = mx + b
=> [tex]y = \frac{1}{9} x[/tex]
Hence, the equation of the line is [tex]y = \frac{1}{9} x[/tex]
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a can of fruit contains 5 ½ cups of fruit.
The suggested serving size is ½ cup.
How many servings are in a can of fruit?
Answers
After doing some mathematical operations we can conclude that there are 11 servings in a fruit can.
What are mathematical operations?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation." The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers. The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out by the arithmetic operators.So, servings in a fruit can:
5½ ÷ ½Now, solve the following as follows:
5½ ÷ ½11/2 ÷ 1/25.5 ÷ 0.511Therefore, after doing some mathematical operations we can conclude that there are 11 servings in a fruit can.
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What is the value of x
3√9+ x = 15
Answers
Answer: 6
Step-by-step explanation: .
Answer:
x=12.92
cube root of 9 Is 2.08 so you minus 15-2.08=12.92
the________ is the side right triangle that is directly across from the right angle
Answers
Juni buys a new car. Her auto loan is $12,000 with an annual interest rate of 3% compounded monthly for 5 years. Her monthly payment is $287. The following table shows the first payment in the amortization schedule.
Explain what the missing values in the table should be, and show your work.
Payment number: 1
Loan Amount: 12,000
Payment: 287
Interest: ???
Principal: ???
Remaining Balance: ???
Answers
The missing values in the first month of payment in the amortization schedule are:
Interest is $30The principal is $257The remaining balance is $11,743.What is an amortization schedule?An amortization schedule is a table that shows the loan amount, the periodic payment, the portion of the regular payment that is the interest and the principal repayment, and the remaining balance after each period.
The amortization schedule presents the above information in an easy format for ready evaluation.
How the missing figures are worked out:Auto Loan = $12,000
Annual interest rate = 3% compounded monthly
Loan period = 60 months (5 years x 12)
Monthly Payment = $287
Interest = $30 ($12,000 x 3% x 1/12)
Principal Repayment = $257 ($287 - $30)
Remaining Balance = $11,743 ($12,000 - $257)
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Phindi is an athlete . as part of her training, she runs around the outside of a circular track that has a radius of 88m. as part of her training, she has to run 12kmon the track. how many circuits of the track will she have to run?
Answers
It takes Phindi to run almost 22 tracks to cover 12kms
Given that,
First you have to figure out the length of the track whihc is circumference of circle ,
r is the radius of circular track which is 88m
The athlete has to run 12km on the track
Circumference of circle = 2πr
Solving circumference will give length of the circular track which is,
Circumference of circle = 2(3.14)(88)
=552.6 meters
If she covers 552.6 m whe runs one circular track then,
1 circular track -------- 552.6 meters
? circular track -------- 12000 meters or 12 kilometers
No of circular tracks = 12000/552.6 = 21.7 tracks
Therefore, It takes Phindi to run almost 22 tracks to cover 12kms
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If 3x - 14 + 3x +9 = 103 what does X equal?
Answers
Anwser is 18
I used a website
Answer: x = 18
Isolating a variable: rearranging the equation to make the variable on side of the equation and the others on the other side
1. Collect like terms
2. Inverse operations to isolate
3. simplify if necessary
Calculations:
[tex]3x -14 +3x +9= 103[/tex]
Collect like terms: [tex]6x -5 =103[/tex]
3x and 3x are alike and -14 +9 are alikeInverse operations:
[tex]6x = 103 +5[/tex]
[tex]6x= 108[/tex]
[tex]\frac{6x}{6}=\frac{108}{6}[/tex]
∴ [tex]x= 18[/tex]
The cross country team ran 1.772 hours yesterday and 1.49 hours today. Each member of the team ran 3.5 miles every hour. How many miles did each member run yesterday?
Answers
The distance that member of the cross country team ran is 6.2 miles yesterday.
How to calculate the amount each team member will pay?Distance is a numerical or qualitative measurement of the distance between two objects or points. Distance can refer to a physical length or an estimate based on other criteria in physics or everyday usage.
The cross-country team ran 1.772 hours yesterday, today they ran 1.49 hours Each member of the team ran 3.5 miles every hour.
The number of miles attained by each member of the team yesterday can be calculated as follows:
3.5 × 1.772= 6.2
Hence for yesterday each member of the team ran for 6.2 miles.
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A glass bottle filled with oil weighs 590 grams. After Sophia uses 200 milliliters of oil, the bottle of oil weighs 400 grams.
Answers
Assuming the question is : How much does x liters/milimeters of oil weigh?
First, we calculate how much mass did the bottle of oil lose : 590 - 400 = 190 (grams)
Since it loses 190 grams after Sophia uses 200 milimeters of oil, 200 milimeters of oil weighs 190 grams (yes.)
-> 1 milimeter of oil weighs : 190/200 = 0.95(grams)
So, to calculate the mass of x *liters* of oil, we take 0,95 x 1000 times x.
For example : To calculate the mass of 22,5 liters of oil, we take 0,95 x 1000 x 22,5 = 21375 (g) or 21.35(kg).
Anna model airplane, the scale is 5 cm equals 2 m. If the models wingspan is 28.5 centimeters camera what is the actual wingspan?
Answers
Answer:
11.4 m
Step-by-step explanation:
2m / 5 cm * 28.5 cm = 11.4 m
Would you be able to help me on this question
Answers
a) From the exercise we can identify 3 unknowns from the 3 funds
• Large Growth = ,LG
,• Small Growth = ,SG
,• Large Value = ,LV
b)
[tex]\begin{gathered} LG+SG+LV=10,000\to(1) \\ LG=SG+2,000\to(2) \end{gathered}[/tex]Find the value of x!
Answers
××1=× 123 =×/1= the value of x is one
find the measure of each missing angle in the parallel lines and transversals below
Answers
The equation is 10x=2x+60
x=15/2
∠CFH=75
∠CBD= 75
We are dealing with parallel lines, which are the lines that are equidistant to each other and never meet, will never meet, when such lines are crossed by another line called the transversal creates many angles such as corresponding angles, vertical angles, alternate interior angles, alternate exterior angles, consecutive angles.
Since, angle CBD and angle CFH are the corresponding angles and they are equal to each other, we are given CBD=2x+60 and CFH = 10x
therefore , 10x=2x+60
=>10x-2x=60
=>8x=60
x=15/2
So, the angle CBD= 2x+60= 2(15/2)+60= 75
and the angle CFH = 10x= 10(15/2)= 75
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PLS HELP I WILL MARK BRAINLEIST
Answers
Volume of the sphere = 17157.28 cubic centimeters
How to calculate the volume of a sphere?
Given:
Diameter (d) = 32
r = d/2 = 16
We know that the volume of a sphere is,
[tex]V=\frac{4}{3} \pi r^{3} \\\\ = \frac{4}{3} (3.14) (16)^{3}\\\\=17157.28 cm^{3}[/tex]
What is the volume of a sphere?
A sphere's capacity is measured by its volume. The sphere has a three-dimensional, rounded shape. Its shape is defined by its three axes, which are the x, y, and z axes. Since the cross-section of the sphere is a circle, the volume in this situation is dependent on the radius or diameter.To learn more about volume of a sphere, refer:
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[tex]\huge\boxed{\sf 17157.28} \\\\\\\displaystyle \sf Converting\ d\ to\ r\\\\r=\frac{d}{2} =\frac{32}{2} =16\\\\Calculating\ the\ volume \\\\V=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi \times 16^{3} \approx 17157.28 \\\\[/tex]
if the base of a rectangle is 12cm and the area is 345 cm², what is the height of the rectangle
Answers
Answer: 28.75 cm
Step-by-step explanation:
Using the formula for the area of a rectangle, we can plug in our known values and solve for the height.
A = B * H
(345 cm²) = (12cm) * H
28.75 cm = H
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